Hallo Rob,

8 or 12 bit digitising?
from screen you can count 32 pixels per division, verically. Having 8 divisions vertically gives 256 pixels, so resolution is 8bit. My be that internally it is operated with higher resolution? Well, what's displayed is 8bit.

4096 samples?
Yes, 4096 samples per channel.

how long can each sample be?
It depends. E.g. 1Gs/sec totally, gives 500Ms/sec for each of the two channels. So, when displaying 100nsec/Div there should be 50 pixels per division. And indeed you can count 50 pixels per division.
If now time base is changed to 200nsec/Div you will also count 50 pixels per division, which results in 250Ms/sec per channel.
Time base can be set to between 100msec/Div and 100nsec/Div in combination with 50MHz/sec totally. For repetitiv-sampling at 1Gs/sec totally, time base can be set to between 200nsec/Div and 20nsec/Div. So, from this data you can find the answer.

There's also a transient recording feature, where sampling interval can be set between 20msec and 2000sec.

Bye,
Kai